Efficient parametrisations for normal linear mixed models
Gelfand, Alan E., Sahu, Sujit K. and Carlin, Bradley P. (1995) Efficient parametrisations for normal linear mixed models. Biometrika, 82, (3), 479-488. (doi:10.1093/biomet/82.3.479).
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The generality and easy programmability of modern sampling-based methods for maximisation of likelihoods and summarisation of posterior distributions have led to a tremendous increase in the complexity and dimensionality of the statistical models used in practice. However, these methods can often be extremely slow to converge, due to high correlations between, or weak identifiability of, certain model parameters. We present simple hierarchical centring reparametrisations that often give improved convergence for a broad class of normal linear mixed models. In particular, we study the two-stage hierarchical normal linear model, the Laird-Ware model for longitudinal data, and a general structure for hierarchically nested linear models. Using analytical arguments, simulation studies, and an example involving clinical markers of acquired immune deficiency syndrome (aids), we indicate when reparametrisation is likely to provide substantial gains in efficiency.
|Digital Object Identifier (DOI):||doi:10.1093/biomet/82.3.479|
|Keywords:||gibbs sampler, hierarchical model, identifiability, laird-ware model, markov chain monte carlo, nested models, random effects model, rate of convergence|
|Subjects:||Q Science > QA Mathematics
H Social Sciences > HA Statistics
|Divisions :||University Structure - Pre August 2011 > School of Mathematics > Statistics
|Accepted Date and Publication Date:||
|Date Deposited:||11 May 2007|
|Last Modified:||31 Mar 2016 11:56|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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